An electronics firm manufactures high-performance drones. The continuous flight time of a 'SkyMaster' drone, T T\,T minutes, is modeled by a normal distribution with a mean of 42 minutes and a standard deviation of 4.5 minutes.
(i) Find P(T<35.5)P(T < 35.5)P(T<35.5).
(a) (ii) Find P(T>50)P(T > 50)P(T>50).
(a) (iii) To achieve an 'Endurance Rating', a drone must fly for a duration between 38 and 48 minutes. Determine the proportion of 'SkyMaster' drones that achieve this rating.
The firm also produces a 'Nano' model. The flight time of the 'Nano' model is normally distributed with mean μ \mu\,μ and standard deviation σ\sigmaσ.
Testing reveals that 10% of these drones have a flight time of less than 25 minutes, and 20% of these drones have a flight time greater than 35 minutes.
Find the value of μ \mu\,μ and the value of σ \sigma\,σ for the 'Nano' drones.
390 exam-style questions on OCR (MEI) A Level Maths 2.4 Probability Distributions, covering 2.4.1 Recognise binomial situations, 2.4.2 Probability of success p, 2.4.3 Calculate binomial probabilities, 2.4.4 Mean of the binomial distribution, 2.4.5 Expected frequencies for binomial, 2.4.6 Probability functions and discrete random variables, 2.4.7 Numerical probabilities for a simple distribution, 2.4.8 Normal distribution as a model (A-level only), 2.4.9 Shape of the Normal curve (A-level only), 2.4.10 Linear transformation and standardising (A-level only), 2.4.11 Symmetry and inflection of Normal curve (A-level only), 2.4.12 Calculate probabilities from a Normal distribution (A-level only), 2.4.13 Model with probability distributions, and 2.4 Probability Distributions. Each one has a worked solution and a mark scheme showing where the marks go.